\documentclass[9pt]{article}
\usepackage{amsmath}
\begin{document}
Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  -3.0 & -2.00 x_{1} & -6.00 x_{2} & -5.00 x_{3} & -8.00 x_{4} & +  8.00 x_{5} & +  7.00 x_{6} & -4.00 x_{7} & +  9.00 x_{8} & +  4.00 x_{9}\\
 x_{11}   &  2.0 & +  8.00 x_{1} & +  9.00 x_{2} &   & -4.00 x_{4} & +  2.00 x_{5} &   & -10.00 x_{7} & +  3.00 x_{8} & -6.00 x_{9}\\
 x_{12}   &  0.0 & -7.00 x_{1} & -5.00 x_{2} & +  8.00 x_{3} & +  2.00 x_{4} &   & + 10.00 x_{6} & +  3.00 x_{7} & -8.00 x_{8} & +  5.00 x_{9}\\
 x_{13}   &  -1.0 & -3.00 x_{1} & -8.00 x_{2} & -8.00 x_{3} & -4.00 x_{4} & -9.00 x_{5} & -6.00 x_{6} & +  7.00 x_{7} & +  4.00 x_{8} & -2.00 x_{9}\\
 x_{14}   &  0.0 & -3.00 x_{1} & -8.00 x_{2} & +  8.00 x_{3} & +  2.00 x_{4} & +  9.00 x_{5} & +  2.00 x_{6} & +  7.00 x_{7} & +  6.00 x_{8} & +  6.00 x_{9}\\
 x_{15}   &  3.0 & +  8.00 x_{1} & -3.00 x_{2} & + 10.00 x_{3} & -7.00 x_{4} & +  6.00 x_{5} & +  6.00 x_{6} & +  6.00 x_{7} & +  9.00 x_{8} & -8.00 x_{9}\\
 x_{16}   &  3.0 & + 10.00 x_{1} & -1.00 x_{2} & -5.00 x_{3} & -5.00 x_{4} & +  1.00 x_{5} & -3.00 x_{6} & -8.00 x_{7} & +  3.00 x_{8} & +  8.00 x_{9}\\
 x_{17}   &  1.0 & +  8.00 x_{1} &   & +  9.00 x_{3} & +  1.00 x_{4} & +  4.00 x_{5} & +  9.00 x_{6} &   & -6.00 x_{8} & -3.00 x_{9}\\
\hline
z    &  0.0  &   & -1.00 x_{2} & +  5.00 x_{3} & -5.00 x_{4} & -3.00 x_{5} & +  3.00 x_{6} & +  2.00 x_{7} &   & +  5.00 x_{9}\\
\end{array}\]
\subsection{Initialization Phase: Dual Problem Solving}
New Objective in primal was changed to : \[ \max\ \sum_{j=1}^{9}\ - x_j \] 
Primal variable $x_j$ corresponds to dual variable $y_j$ for $j = 1,\ldots,17$
Dual Dictionary (with objective changed is): 
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.0 & +  2.00 y_{10} & -8.00 y_{11} & +  7.00 y_{12} & +  3.00 y_{13} & +  3.00 y_{14} & -8.00 y_{15} & -10.00 y_{16} & -8.00 y_{17}\\
 y_{2}   &  1.0 & +  6.00 y_{10} & -9.00 y_{11} & +  5.00 y_{12} & +  8.00 y_{13} & +  8.00 y_{14} & +  3.00 y_{15} & +  1.00 y_{16} &   \\
 y_{3}   &  1.0 & +  5.00 y_{10} &   & -8.00 y_{12} & +  8.00 y_{13} & -8.00 y_{14} & -10.00 y_{15} & +  5.00 y_{16} & -9.00 y_{17}\\
 y_{4}   &  1.0 & +  8.00 y_{10} & +  4.00 y_{11} & -2.00 y_{12} & +  4.00 y_{13} & -2.00 y_{14} & +  7.00 y_{15} & +  5.00 y_{16} & -1.00 y_{17}\\
 y_{5}   &  1.0 & -8.00 y_{10} & -2.00 y_{11} &   & +  9.00 y_{13} & -9.00 y_{14} & -6.00 y_{15} & -1.00 y_{16} & -4.00 y_{17}\\
 y_{6}   &  1.0 & -7.00 y_{10} &   & -10.00 y_{12} & +  6.00 y_{13} & -2.00 y_{14} & -6.00 y_{15} & +  3.00 y_{16} & -9.00 y_{17}\\
 y_{7}   &  1.0 & +  4.00 y_{10} & + 10.00 y_{11} & -3.00 y_{12} & -7.00 y_{13} & -7.00 y_{14} & -6.00 y_{15} & +  8.00 y_{16} &   \\
 y_{8}   &  1.0 & -9.00 y_{10} & -3.00 y_{11} & +  8.00 y_{12} & -4.00 y_{13} & -6.00 y_{14} & -9.00 y_{15} & -3.00 y_{16} & +  6.00 y_{17}\\
 y_{9}   &  1.0 & -4.00 y_{10} & +  6.00 y_{11} & -5.00 y_{12} & +  2.00 y_{13} & -6.00 y_{14} & +  8.00 y_{15} & -8.00 y_{16} & +  3.00 y_{17}\\
\hline
z    &  -0 & +  3.00 y_{10} & -2.00 y_{11} &   & +  1.00 y_{13} &   & -3.00 y_{15} & -3.00 y_{16} & -1.00 y_{17}\\
\end{array}\]
Initialization succeeded in finding final dual dictionary with 4 pivots
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  2.5501618123 & -0.15 y_{8} & -0.13 y_{11} & -0.57 y_{6} & -0.83 y_{7} & -4.85 y_{14} & -17.75 y_{15} & -2.08 y_{16} & -12.23 y_{17}\\
 y_{2}   &  3.71844660194 & -0.72 y_{8} & +  1.99 y_{11} & -0.68 y_{6} & -1.32 y_{7} & -6.90 y_{14} & -15.47 y_{15} & + 11.41 y_{16} & -1.81 y_{17}\\
 y_{3}   &  2.15533980583 & -0.91 y_{8} & +  1.73 y_{11} & +  0.20 y_{6} & -0.45 y_{7} & -16.19 y_{14} & -19.67 y_{15} & +  5.22 y_{16} & -1.69 y_{17}\\
 y_{4}   &  2.52750809061 & -0.81 y_{8} & +  5.49 y_{11} & -0.33 y_{6} & -0.39 y_{7} & -10.24 y_{14} & -4.59 y_{15} & +  6.70 y_{16} & +  0.89 y_{17}\\
 y_{5}   &  1.48220064725 & +  0.13 y_{8} & +  8.49 y_{11} & +  0.40 y_{6} & -1.01 y_{7} & -14.52 y_{14} & -8.52 y_{15} & +  6.26 y_{16} & -1.12 y_{17}\\
 y_{12}   &  0.11003236246 & +  0.02 y_{8} & +  0.72 y_{11} & -0.06 y_{6} & -0.07 y_{7} & -0.47 y_{14} & -0.60 y_{15} & +  0.78 y_{16} & -0.70 y_{17}\\
 y_{13}   &  0.171521035599 & -0.05 y_{8} & +  1.03 y_{11} & -0.00 y_{6} & -0.12 y_{7} & -1.13 y_{14} & -1.18 y_{15} & +  0.81 y_{16} & +  0.26 y_{17}\\
 y_{10}   &  0.132686084142 & -0.07 y_{8} & -0.15 y_{11} & -0.06 y_{6} & -0.01 y_{7} & -0.58 y_{14} & -1.01 y_{15} & +  0.00 y_{16} & -0.07 y_{17}\\
 y_{9}   &  0.26213592233 & +  0.08 y_{8} & +  5.04 y_{11} & +  0.53 y_{6} & +  0.12 y_{7} & -3.58 y_{14} & + 12.68 y_{15} & -10.31 y_{16} & +  7.27 y_{17}\\
\hline
z    &  0.569579288026 & -0.26 y_{8} & -1.41 y_{11} & -0.17 y_{6} & -0.14 y_{7} & -2.88 y_{14} & -7.21 y_{15} & -2.18 y_{16} & -0.94 y_{17}\\
\end{array}\]
Primal Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  0.262944983819 & +  0.15 x_{1} & +  0.72 x_{2} & +  0.91 x_{3} & +  0.81 x_{4} & -0.13 x_{5} & -0.02 x_{12} & +  0.05 x_{13} & +  0.07 x_{10} & -0.08 x_{9}\\
 x_{11}   &  1.41343042071 & +  0.13 x_{1} & -1.99 x_{2} & -1.73 x_{3} & -5.49 x_{4} & -8.49 x_{5} & -0.72 x_{12} & -1.03 x_{13} & +  0.15 x_{10} & -5.04 x_{9}\\
 x_{6}   &  0.169093851133 & +  0.57 x_{1} & +  0.68 x_{2} & -0.20 x_{3} & +  0.33 x_{4} & -0.40 x_{5} & +  0.06 x_{12} & +  0.00 x_{13} & +  0.06 x_{10} & -0.53 x_{9}\\
 x_{7}   &  0.137540453074 & +  0.83 x_{1} & +  1.32 x_{2} & +  0.45 x_{3} & +  0.39 x_{4} & +  1.01 x_{5} & +  0.07 x_{12} & +  0.12 x_{13} & +  0.01 x_{10} & -0.12 x_{9}\\
 x_{14}   &  2.8786407767 & +  4.85 x_{1} & +  6.90 x_{2} & + 16.19 x_{3} & + 10.24 x_{4} & + 14.52 x_{5} & +  0.47 x_{12} & +  1.13 x_{13} & +  0.58 x_{10} & +  3.58 x_{9}\\
 x_{15}   &  7.20631067961 & + 17.75 x_{1} & + 15.47 x_{2} & + 19.67 x_{3} & +  4.59 x_{4} & +  8.52 x_{5} & +  0.60 x_{12} & +  1.18 x_{13} & +  1.01 x_{10} & -12.68 x_{9}\\
 x_{16}   &  2.18122977346 & +  2.08 x_{1} & -11.41 x_{2} & -5.22 x_{3} & -6.70 x_{4} & -6.26 x_{5} & -0.78 x_{12} & -0.81 x_{13} & -0.00 x_{10} & + 10.31 x_{9}\\
 x_{17}   &  0.944174757282 & + 12.23 x_{1} & +  1.81 x_{2} & +  1.69 x_{3} & -0.89 x_{4} & +  1.12 x_{5} & +  0.70 x_{12} & -0.26 x_{13} & +  0.07 x_{10} & -7.27 x_{9}\\
\hline
z    &  -0.569579288026 & -2.55 x_{1} & -3.72 x_{2} & -2.16 x_{3} & -2.53 x_{4} & -1.48 x_{5} & -0.11 x_{12} & -0.17 x_{13} & -0.13 x_{10} & -0.26 x_{9}\\
\end{array}\]
Primal Dictionary with original objective is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  0.262944983819 & +  0.15 x_{1} & +  0.72 x_{2} & +  0.91 x_{3} & +  0.81 x_{4} & -0.13 x_{5} & -0.02 x_{12} & +  0.05 x_{13} & +  0.07 x_{10} & -0.08 x_{9}\\
 x_{11}   &  1.41343042071 & +  0.13 x_{1} & -1.99 x_{2} & -1.73 x_{3} & -5.49 x_{4} & -8.49 x_{5} & -0.72 x_{12} & -1.03 x_{13} & +  0.15 x_{10} & -5.04 x_{9}\\
 x_{6}   &  0.169093851133 & +  0.57 x_{1} & +  0.68 x_{2} & -0.20 x_{3} & +  0.33 x_{4} & -0.40 x_{5} & +  0.06 x_{12} & +  0.00 x_{13} & +  0.06 x_{10} & -0.53 x_{9}\\
 x_{7}   &  0.137540453074 & +  0.83 x_{1} & +  1.32 x_{2} & +  0.45 x_{3} & +  0.39 x_{4} & +  1.01 x_{5} & +  0.07 x_{12} & +  0.12 x_{13} & +  0.01 x_{10} & -0.12 x_{9}\\
 x_{14}   &  2.8786407767 & +  4.85 x_{1} & +  6.90 x_{2} & + 16.19 x_{3} & + 10.24 x_{4} & + 14.52 x_{5} & +  0.47 x_{12} & +  1.13 x_{13} & +  0.58 x_{10} & +  3.58 x_{9}\\
 x_{15}   &  7.20631067961 & + 17.75 x_{1} & + 15.47 x_{2} & + 19.67 x_{3} & +  4.59 x_{4} & +  8.52 x_{5} & +  0.60 x_{12} & +  1.18 x_{13} & +  1.01 x_{10} & -12.68 x_{9}\\
 x_{16}   &  2.18122977346 & +  2.08 x_{1} & -11.41 x_{2} & -5.22 x_{3} & -6.70 x_{4} & -6.26 x_{5} & -0.78 x_{12} & -0.81 x_{13} & -0.00 x_{10} & + 10.31 x_{9}\\
 x_{17}   &  0.944174757282 & + 12.23 x_{1} & +  1.81 x_{2} & +  1.69 x_{3} & -0.89 x_{4} & +  1.12 x_{5} & +  0.70 x_{12} & -0.26 x_{13} & +  0.07 x_{10} & -7.27 x_{9}\\
\hline
z    &  0.782362459547 & +  3.37 x_{1} & +  3.68 x_{2} & +  5.28 x_{3} & -3.23 x_{4} & -2.19 x_{5} & +  0.32 x_{12} & +  0.25 x_{13} & +  0.18 x_{10} & +  3.16 x_{9}\\
\end{array}\]
\section{Optimization Phase Simplex}
Starting Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  0.262944983819 & +  0.15 x_{1} & +  0.72 x_{2} & +  0.91 x_{3} & +  0.81 x_{4} & -0.13 x_{5} & -0.02 x_{12} & +  0.05 x_{13} & +  0.07 x_{10} & -0.08 x_{9}\\
 x_{11}   &  1.41343042071 & +  0.13 x_{1} & -1.99 x_{2} & -1.73 x_{3} & -5.49 x_{4} & -8.49 x_{5} & -0.72 x_{12} & -1.03 x_{13} & +  0.15 x_{10} & -5.04 x_{9}\\
 x_{6}   &  0.169093851133 & +  0.57 x_{1} & +  0.68 x_{2} & -0.20 x_{3} & +  0.33 x_{4} & -0.40 x_{5} & +  0.06 x_{12} & +  0.00 x_{13} & +  0.06 x_{10} & -0.53 x_{9}\\
 x_{7}   &  0.137540453074 & +  0.83 x_{1} & +  1.32 x_{2} & +  0.45 x_{3} & +  0.39 x_{4} & +  1.01 x_{5} & +  0.07 x_{12} & +  0.12 x_{13} & +  0.01 x_{10} & -0.12 x_{9}\\
 x_{14}   &  2.8786407767 & +  4.85 x_{1} & +  6.90 x_{2} & + 16.19 x_{3} & + 10.24 x_{4} & + 14.52 x_{5} & +  0.47 x_{12} & +  1.13 x_{13} & +  0.58 x_{10} & +  3.58 x_{9}\\
 x_{15}   &  7.20631067961 & + 17.75 x_{1} & + 15.47 x_{2} & + 19.67 x_{3} & +  4.59 x_{4} & +  8.52 x_{5} & +  0.60 x_{12} & +  1.18 x_{13} & +  1.01 x_{10} & -12.68 x_{9}\\
 x_{16}   &  2.18122977346 & +  2.08 x_{1} & -11.41 x_{2} & -5.22 x_{3} & -6.70 x_{4} & -6.26 x_{5} & -0.78 x_{12} & -0.81 x_{13} & -0.00 x_{10} & + 10.31 x_{9}\\
 x_{17}   &  0.944174757282 & + 12.23 x_{1} & +  1.81 x_{2} & +  1.69 x_{3} & -0.89 x_{4} & +  1.12 x_{5} & +  0.70 x_{12} & -0.26 x_{13} & +  0.07 x_{10} & -7.27 x_{9}\\
\hline
z    &  0.782362459547 & +  3.37 x_{1} & +  3.68 x_{2} & +  5.28 x_{3} & -3.23 x_{4} & -2.19 x_{5} & +  0.32 x_{12} & +  0.25 x_{13} & +  0.18 x_{10} & +  3.16 x_{9}\\
\end{array}\]


 $ x_{1} $ enters and Unbounded Dictionary!


 $ x_{1} $ enters and Unbounded Dictionary!
\end{document}
